[r-t] Extension of TDMMs
pabs at cantab.net
Thu Aug 12 19:13:37 UTC 2004
Richard Smith <richard at ex-parrot.com> wrote at 14:52:31 on Tue, 10 Aug
>Warkworth Surprise Minor with a mode-3 BC extension above a mode-1 EF
>extension gives the following surprise major and royal methods.
>At higher stages, however, you always get irregular lead ends (which
>are frequently differential hunters).
Of symmetrical methods with the treble and one other bell pivoting at
the half-lead, the proportion that have plain bob lead ends at stage n
(even) is 1 in (n-3)(n-5)...3, giving
I suppose that given the number of possible Minor methods and potential
extension paths, a chance of roughly 1 in 5000 that a random choice will
give PB lead ends at three stages means that such an example is almost
inevitable - but is there a sufficiently large sample for four or more?
Does the number of additional possibilities as the stage increases
compensate for the much smaller chance of a random occurrence?
The feature that ultimately causes irregular lead ends in the above
example is that the extending section produces plain hunting on an
expanding number of bells: such hunting at a faster rate than the treble
causes each bell to turn round eventually, disrupting the coursing
order. The same problem is evident in London.
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